I’ll answer the last question about 𝛾 and defer to Carlos to address the questions about the Linear Time Varying Dynamical System in MOST.
When solving a multiperiod stochastic problem in MOST, we assume that, for the sake of the optimization, we are unable to adequately evaluate the impact of decisions taken after low probability events (contingencies) occur. We optimize in order to handle the contingency, but if it occurs we assume you will be re-running your optimization with new information in order to get back on track. So, in MOST, when considering contingencies, each contingency has a certain probability of occurring. Let’s suppose we are dealing with a 3-period problem with a single base case, and single contingency in each period, each with a conditional probability of occurring of 1%. That is 𝜓0tjk = 0.01 for all t, j and k. This means that in period 1, the probability of a contingency is 1% and the probability of being in the base case, and transitioning to period 2 is 99%. So 𝛾2 is 0.99. The conditional probability of a contingency happening in period 2 (given that one didn’t happen in period 1) is also 1%, meaning that the unconditional probability of being in the contingency state in period 2 is 0.99*0.01. And the unconditional probability of being in the base state in period 2 and transitioning to period 3, is 0.99^2, this is 𝛾3. I hope this helps, Ray > On Apr 12, 2018, at 6:10 AM, Shady Mamdouh <[email protected]> > wrote: > > > > Sent from Yahoo Mail on Android > <https://overview.mail.yahoo.com/mobile/?.src=Android> > On Tue, Apr 10, 2018 at 4:34, Shady Mamdouh > <[email protected]> wrote: > ,Hi MATPOWER friends > > -I want to understand the "Linear Time Varying Dynamical System in MOST" in > some depth as the only example on it in the manual, "t_most_w_ds.m", is not > explained neither in the MOST manual nor in MATLAB help. > > -I understood that variables depend on power dispatches can be constrained > using this feature like emissions or water level of hydro units but an > example explaining this is appreciated or explanation of "t_most_w_ds.m" > example. > > -Also, can I know more examples of variables that can be used with this > feature ? > > -Finally, If the parameter named "Gamma ɣ" be deeply explained I would be > thankful. > (Gamma ɣ :Probability of making it to period "t" without branching of the > central path in a contingency in periods 1.......... t-1.) > > Thanks in advance > > Shady M. Sadek > PhD Student, Ain Shams Univ., Cairo, Egypt. > > > <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> > Virus-free. www.avg.com > <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> > <x-msg://54/#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
